CSR Benchmark Test-Case Results Paul Emma SLAC January 14, 2001 BERLIN CSR Workshop

Chicane CSR Test-Case Use line-charge CSR    transient model described in LCLS-TN-01-12… (Stupakov/Emma, Dec. 2001) [same now used in Elegant] …based on TESLA-FEL-96-14 (Saldin et al., Nov. 1996) (T566 included, no ISR* added) * incoherent synchrotron radiation

Initial Gaussian Distribution Prior to Chicane perfectly linear correlation sE/E0 = 0.72 %  bunch head ss = 200 mm E0 = 5 GeV

Second Order Compression Included: T566 /mm T566  -3R56/2 leads to slight bunch shape distortion after drift-3 before drift-3

Beta and Dispersion Functions ‘CSR-altered’ bx ‘linear’ bx hx-max  267 mm ‘linear’ hx

Bunch Length and R56 ss0 = 200 mm ss = 20 mm R56 = -25 mm B1 B2 B3 B4

Final s-d phase space (gaussian input) sE/E0 = 0.716 %  bunch head ss = 20.3 mm

Energy Spread and Emittance (gaussian) B1 B2 B3 B4 E /E0  -0.043% sd  0.021% B1 B2 B3 B4 gex  1.52 mm

Total RMS Relative Energy Spread (including ‘chirp’) B1 B2 B3 B4

Chicane CSR-wake Movie (gaussian)

Chicane CSR-integrated-wake (gaussian)

Final x-x Phase Space (gaussian input) ge  1.52 mm geCSR  0.145 mm ge0 = 1.00 mm bopt  1.37 m aopt  -1.10

Final x-x Phase Space (gaussian & optimal b0, a0) emittance growth can be reduced by choosing optimal b-functions ge  1.15 mm geCSR  0.145 mm b  bopt a  aopt ge0 = 1.00 mm

Beta and emittance (gaussian & optimal b0, a0) too big? bmin  0.6 m b  bopt a  aopt gex  1.15 mm

CSR wakefields (gaussian  bend-1 to drift-2) L = 0.4 m drift-1 (20) L = 5 m Nbin = 600, smoothed over 4 bend-2 (10) L = 0.4 m drift-2 (10) L = 1 m

CSR wakefields (gaussian  bend-3 to drift-4) L = 0.4 m drift-3 (40) L = 5 m bend-4 (20) L = 0.4 m drift-4 (20) L = 2 m

Compressing Uniform Distribution

Final s-d phase space – Uniform input dist. sE/E0 = 0.720 % ss = 20.2 mm

Energy Spread and Emittance (uniform) E /E0  -0.046% sd  0.007% emittance growth reduced compared to gaussian gex  1.12 mm

Chicane CSR-wake Movie – Uniform Dist.

Chicane CSR-integrated-wake – Uniform Dist.

Final x-x Phase Space (uniform input) ge  1.12 mm geCSR  0.07 mm ge0 = 1.00 mm bopt  3.9 m aopt  -0.51

CSR wakefields (uniform  bend-1 to drift-2) L = 0.4 m drift-1 (20) L = 5 m Nbin = 600, smoothed over 4 bend-2 (10) L = 0.4 m drift-2 (10) L = 1 m

CSR wakefields (uniform  bend-3 to drift-4) L = 0.4 m drift-3 (40) L = 5 m bend-4 (20) L = 0.4 m drift-4 (20) L = 2 m

Betatron Amplitude per Bunch Slice gaussian l(s) uniform l(s)

Final s-d phase space - Single-Bend sE/E0 = 0.011 % ss = 20.1 mm

Energy Spread and Emittance – Single Bend steady-state bend magnet sd = 0.011% (24ssR2)1/3

CSR-Wake Movie - Single-Bend

LCLS BC2 CSR-integrated-wake (tracked dist.)